Armature issue Importing an FBX file from Unreal Engine to Blender
This is not a mess, but an ordinary FK rig, based on "joints" instead of "bones". You can think of joints as the same entity of the Head of a Blender bone. As the location of the tail is not taken into account, the "bones" are oriented in the most useful way for editing (like best alignement with world coordinates and main rotation on the X axis). 

If FK animation is enough, you can do your animation directly. 

If you need a more advanced rig, you should build it using the exact location of the joints, then set a serie of copy rotation constaints from the advanced rig to the UE rig, so that the UE rig become your deforming bones, while the advanced will be control bones only. 

At the end you will be able to bake your action using visual keying, only selected bones, and clear constraints options, so that the baked action will perfectly work with the UE rig only.

If this procedure sounds scary, start with an experiment with a simple animation of one body part only (i.e. one leg), and see if you can get it work.